2009
BRIDGES WORKSHOPS: CREATIVITY AND LEARNING
Call for papers
(SUBMISSION: http://bridgesmathart.org/bridges-2009/2009-call-for-papers/submission/)
As well as the normal lecture-type presentations, the Bridges conference includes longer workshop sessions. These provide participants with opportunities to engage in some practical activities, which they can go on to use, or develop, as artists, educators, or facilitators of their own workshops.
Submissions can be either a short (two pages) proposal describing the practical activity, or a longer (four, six, or eight pages, like other Bridges papers) detailed explanation and/or discussion of content that has not appeared before. It is helpful to include learning objectives, whenever appropriate.
The workshop could be organised as a short introductory presentation followed by some quite prescriptive, hands-on activity, or by more open-ended explorations of the theme, or it could be organised around activity instructions (worksheet) with support from the facilitator, without the need for a detailed introduction. Other less conventional structures are possible, and one of the objectives of the session might be to model, or develop, such new approaches.
There are no constraints on workshop content provided that it falls within the general aims of Bridges, and demonstrates some link between mathematics and the arts, but submissions are sought in particular that would be of value to educators. There could be less emphasis on mathematical or artistic originality if instead some innovative teaching approach is modelled.
http://bridgesmathart.org/bridges-2009/2009-call-for-papers/submission/
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San Sebastian, Spain July 24 - July 27, 2007 |
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Cube (3, 1) with wrapped loop |
Exploring Cubes Woven on the Skew Felicity Wood, www.felicitywood.co.uk
Baskets woven from strips folded up from the base at 90° or 45° are well known. However, forms made by folding up at other angles have been little explored. Weaving a cube (a closed form), as opposed to a ‘basket’ (an open vessel), results in some mathematically interesting and aesthetically pleasing results. Rather than weaving cubes, workshop participants will construct cubes using nets provided, printed on card. It will then be possible to discover some of their characteristics, to answer some questions, and perhaps pose some further questions. There will be a review of ethnographic and artist-made forms woven on the skew. There will also be handling pieces: cubes woven on the skew using a variety of materials – expressions of the underlying mathematics. |
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Digit-sum spiral |
Using Art To Teach Maths * Using Maths
To Create Art In recent years, there has been a move away from approaching topics such as number and algebra, shape and space, probability, and so on, as distinct units of work. Alternative approaches focus on the connections between different areas of maths, using a variety of techniques to explore these. The activities covered in this workshop can be used to give students experience across all these mathematical areas while also linking them to art, history, and other curriculum areas. Delegates will have hands-on experience of up to six different activities, which they will be able to explore at their own pace during the workshop. There will also be opportunities to discuss implications for classroom practice, and ways in which the ideas could be used and extended for students of different abilities and with varying interests. |
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Six-pointed stars |
From Folding and Cutting to Geometry
and Algorithms:
Drawing upon visual forms of expression
prevalent in Islamic arts and architecture, this workshop offers
hands-on experience for understanding basic concepts in geometry, with
reference to algorithms in processes of pattern-making. Art teachers and
math educators may learn a variety of strategies for classroom teaching,
adaptable for K-12, to acquaint students with principles underlying
patterns in Islamic art. Such patterns relate to the history of
mathematics at a time when Baghdad was an intellectually vibrant center
of patronage, and al-Khwarezmi was engaged in the development of what we
now call algebra and algorithms. Students may explore these ideas
through their own experimentation, and relate their experiences to means
of transmission of newly emergent mathematical ideas in the 9th and 10th
centuries of our era. |
 Leonardo’s Claw |
Imaginative Quilted Geometric
Assemblages
Quilts serve as a visual introduction to mathematical objects that allow students to explore mathematical art as they gain geometric insights. From Plato’s dissection in the fourth century and Leonardo da Vinci’s curvilinear shapes in the fifteenth century to Mascheroni constructions of the eighteenth century, these quilt designs and hands-on constructions will engage the viewer in mathematical visualization and problem solving. With each compass construction a corresponding completed quilt will be shown. No sewing is necessary. |
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Zome Workshop How to conduct a Zome workshop for students, teachers or parents. Discusses the discovery learning philosophy, preparing for the workshop, conducting the workshop, follow-up activities and available resources for educators. If you want to get kids excited about mathematics, but don’t know where to start, try a Zome workshop. Zome is a powerful manipulative that applies to many of the (US) national standards (1) and integrates with other core subjects such as science and language arts. And it’s fun! Here’s some structure and content developed for K-8 gifted students in the summer of 2006. Based on the “discovery learning” model, it can break the ice in the classroom, facilitate lot of learning, and leave students begging for more! |
Mod 3 clock |
Math/Art Projects In this hands-on workshop, participants will use mathematical concepts as a framework for creating their own math/art projects. In one project, participants will use modular arithmetic addition and multiplication tables for the underlying structure of project. Another project uses translations and reflections on a square grid and circular grid to create an anamorphic art picture. Handouts for the projects will be provided so that participants can use the ideas in their own classrooms. |
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Gharara Pajamas |
The Geometry of
Asian Trousers
This workshop will explore the simple geometry developed over the centuries by Asian trousers without measurements. They discovered ways of cutting and structuring fabric with extraordinary economy to achieve maximum effect with minimum waste; a valuable attribute today. The techniques are useful for the teaching of geometry and proportion without the perils of number. Actual garments will be used for reference. |
 2 cubes separated with 8 slotted edges for a hypercube |
Building Models to Transition From
Dimension to Dimension Physical models are valuable for conveying spatial concepts in geometry. In this paper, I discuss how to build 4 models which transition between spatial dimensions 0 to 1, 1 to 2, 2 to 3, and 3 to 4. Supplies for these models are bungee cord and PCV pipe and connectors. Another supply is a hollow plastic sphere made from two hemispheres. These supplies cost me less than $60. The tools used are a measuring tape, a jig saw, a circular saw, a sander, a drill and bits, a rasp and scissors. A teacher who is proficient with power tools is capable of safely producing the pieces for these models. Students under a teacher’s supervision are fully capable of assembling and moving these models. Students work together to expand their understanding of space by assembling and moving these models. |
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2006
London, UK
August 4-9, 2006
Workshops:
Zafer Sagdic, Mujdem Vural, & Gokce Tuna Taygun: Workshop For K-12 Teachers: Understanding The Mathematics Based Formulation On Dome Tessellation In Architect Sinan’s Mosques Design
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ABSTRACT: In history, the reasons and the results are important are always related with each other. Sometimes for better understanding, the reasons and results of socio-cultural based relations should be researched on history education. The history of architecture gives lots of clues on that point of view. The aim of this workshop is to understand the reason-result relationship on the creation of dome tessellation of architect Sinan -while designing structure for a specific dimension- by interactive education. To fulfill this aim, the workshop will evaluate the usage of the dome structure in Sinan’s mosques as the result of technology and material. |
Paul Stang: Mandala and 5, 6 and 7 fold Division of the Circle
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ABSTRACT: Participants will learn to divide circles by 5, 6 and 7 to create basic art forms known as Mandalas, relating them to platonic shapes, phi and historical usage in Eastern and Western cultures, providing fascinating bridges between mathematics and art and architecture, history, and science. These techniques can be used to demonstrate fractions, angles, trigonometric relations, and fractals. |
Susan Happersett: Mathematical Book Forms for Teachers
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ABSTRACT: The sequential properties of basic mathematics facilitate the creation of math art book forms. This workshop presents three book forms with mathematical significance for school teachers. _ developing 2D/3D connections |
Evan G. Evans: A Geometric Inspection of Pennsylvanian Dutch Hex Signs
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ABSTRACT: This paper discusses the mathematics that is involved in the construction of “Hex Signs” and describes the construction of such signs using Geometry Sketchpad. Hex Signs are circular discs with intricate geometric designs with specific meanings that were hung on barns in the “Pennsylvania Dutch” region of the United States. Common designs include: Rosettes, Birds, and Star Polygons. |
Michael Round: The Arete of Line Designs
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ABSTRACT: This workshop will explore the historical (including the George Boole connection), philosophical, and pedagogical nature of line designs, with a focus on good designs and what constitutes the proper context / good environment ensuring "joy in work" is realized, now and in the future. |
Virginia Usnick & Marilyn Sue Ford: Moving Beyond Geometric Shapes: Other Connections Between Mathematics and the Arts for Elementary-grade Teachers
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ABSTRACT: When classroom teachers are asked to identify connections between mathematics and art, they typically refer to geometric concepts. In an attempt to broaden their understanding of potential connections, this paper presents activities that involve common vocabulary, probability, and imagery. |
Laura Shea: The Plato Bead—A Bead Dodecahedron
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ABSTRACT: Explore a different type of frame polyhedron—one made from beads. Create a bead dodecahedron (The Plato Bead) and learn several color patterns and shape variations. |
Stephen Luecking: Creating Sliceforms with 3D Modelers
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ABSTRACT: This tutorial and workshop provides the novice with the tools and procedures for modeling and physically constructing mathematical models known as sliceforms, using their PC, a printer, craft knife, glue, and paperboard. |
Jean-Marc Castera: Playing with the Zellij Laser Multipuzzle
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ABSTRACT: "Zellij multipuzzle" is a set of 669 zellij-style tiles used as an introduction to the art of geometrical arabesque. Playing with it provide a direct immersion into the galaxy of zellij. |
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Ergun Akleman & Vinod Srinivasan: Topological Mesh Modeling
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ABSTRACT: This workshop will present Topological Mesh Modeling with hands-on experiments using our topological modeler, TopMod. TopMod provides a wide variety of interactive techniques that allow the creation of unusual and interesting shapes by changing the topology of 2-manifold meshes. |
Ergun Akleman, Ahmet Koman & Tevfik Akgün: Paper Sculptures with Vertex Deflection
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ABSTRACT: This workshop is about vertex deflection and Gauss-Bonnet Theorem. The workshop will show how to create sculptor Ilhan Koman's mathematically motivated developable surfaces and then how to construct a variety of shapes creating saddle, maxima, and minima using nip and tuck. |
Robert McDermott: Building Simple and not so Stick Models
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ABSTRACT: Physical models are invaluable for conveying concepts in geometry. This is an explanation of how to build stick models based on Platonic polyhedra. |
Tomás García-Salgado: Vermeer’s the Music Lesson in Modular Perspective
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ABSTRACT: Reflecting on Vermeer's painting of The Music Lesson, the author will demonstrate the basic use of the RMS90 Modular Scale to directly deduce all the elements of the scene in perspective. (Click on the picture to see full size!) |
Some useful websites that I noticed during Bridges 2006:
Indra's Pearls - http://klein.math.okstate.edu/IndrasPearls/
July, 2007
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Maintained by:
Mara Alagic |
